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In a production process, a total number of 50 items were produced by machines M1, M2 and M3. Of those items being produced, 27 were
In a production process, a total number of 50 items were produced by machines M1, M2 and M3. Of those items being produced, 27 were made by machine M1, 13 were made by M2, and 10 were made by M3. The three machines work independently, however, they do not work perfectly. From the past experience, 9% of the items produced by M1 are defective, 7% of the items produced by M2 are defective, and 4% of the items produced by M3 are defective. (a) Given that a randomly selected item is non-defective, what is the probability that it is produced by machine M2? (b) If two items which are not produced by machine M3 are selected at random without replacement, what is the probability that at least one of them is non-defective
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